The present invention is directed to kinematic couplings, particularly to such couplings having surfaces to exactly constrain the six degrees of freedom of a rigid body, and more particularly to a three tooth kinematic coupling having three line contracts which increases the area of contact, reduces localized stress, and increases stiffness and load capacity.
Kinematic couplings have long been known to provide an economical and dependable method for attaining high repeatability in fixtures. Properly designed kinematic couplings are deterministic: they only make contact at a number of points equal to the number of degrees of freedom that are to be restrained. Being deterministic makes performance predictable and also helps to reduce design and manufacturing costs. On the other hand, contact stresses in kinematic couplings are often very high and no elastrohydrodynamic lubrication layer exists between the elements that are in point contact; thus for high-cycle applications, it is advantageous to have the contact surfaces made from corrosion-resistant materials (e.g., ceramics). When non-stainless steel components are used, one must wary of fretting at the contact interfaces, so steel couplings should only be used for low-cycle applications.
Submicron repeatability is common because a kinematic coupling provides the minimum number of contact surfaces required to exactly constrain the six degrees of freedom of a rigid body. Analytically, a kinematic coupling is statically determinant except for a small uncertainty regarding friction between the contacting surfaces.
Previously, there existed two general types of kinematic couplings. Each type uses three spheres or balls attached to one part which come to rest on six surfaces on the mating part. This gives nearly ideal kinematics at the price of very high localized stresses. The first of these two types of kinematic couplings is commonly called a Kelvin Clamp. In this coupling, the three balls rest respectively in a tetrahedral socket, a vee-groove aligned to the socket, and a flat plane. The load capability of the Kelvin Clamp is almost always limited by high stress at the interface between the ball and the flat. The second type of kinematic coupling differs by having three vee-grooves to receive the three balls. The grooves usually, but not necessarily, align to a point between them. When the grooves are manufactured as a gothic arch to increase the actual area of contact, the stiffness and load capacity of the three-ball-and-vee coupling are greatly improved over those of the Kelvin Clamp. These prior known kinematic couplings are exemplified in A. Slocum, Precision Machine Design, Prentice Hall, 1992, pp. 401-402; and D. L. Blanding, Principles of Exact Constraint Mechanical Design, Eastman Kodak Co., 1992, pp. 28-29.
The kinematic coupling of the present invention differs from the above-described prior approaches in that it utilizes a three tooth arrangement based on having three theoretical line contacts formed by mating teeth rather than six theoretical point contacts. One could consider six points arranged in pairs to define three lines of contact, but this fact has not been previously used to increase the actual area of contact and thus increase the coupling's stiffness and load capacity. Tooth type couplings, often referred to as positive clutches, are known as exemplified by Machinery Handbook, 24th Edition, Couplings and Clutches, Industrial Press, 1992, pp. 2237-2239. However, these prior teeth type couplings require more than three teeth. Also, another previous tooth type coupling, e.g., Hirth couplings, exemplified in (citation showing a Hirth coupling), have not been kinematic because their primary application has been angular indexing that generally requires more than three teeth. A Hirth coupling with only three teeth would be semi-kinematic but still would require highly precise and specialized machine tools to manufacture the mating tooth profiles. The three tooth kinematic coupling is also semi-kinematic but its tooth form allows an extra degree of freedom that greatly simplifies manufacture. The machine tool needs only to have precise straight line motion to produce teeth that mate properly.